Q: A block of mass $$m is $$projected up a rough incline with initial speed $$v_0. $$The coefficient of kinetic friction is $$\mu_k. $$What is the distance $$d$$ the block travels up the incline before coming to rest?

$$d = \dfrac{v_0$^2}{2g(\sin\theta + \mu_k \cos\theta)}$$

Q: A volleyball player hits a ball at height $$H$$ above the ground with initial speed $$v_0 at $$angle $$\theta$$ above the horizontal. Neglecting air resistance, what is the time $$t it $$takes for the ball to reach the same height $$H$$ again?

$$t = \dfrac{2v_0 \sin\theta}{g}$$

Question 1

A particle moves along the x-axis such that its position is given by $$x(t) = 4t^3$ - 3t^2$ + 2t - 5. $$What is the acceleration of the particle at $$t = 2 s$$?

Accepted Answer

$$a(2) = 48 m/s$^2$$

Question 2

A car starts from rest and accelerates uniformly at $$2 m/s$^2$$ for $$5$$ seconds. What is the total distance traveled by the car in this time?

Accepted Answer

$$50 m$$

Question 3

A ball is thrown vertically upward with an initial speed $$v_0$$ from the ground. Neglecting air resistance, what is the speed of the ball when it returns to the ground?

Accepted Answer

Equal to $$v_0$$

Question 4

A block of mass $$m$$ slides down a frictionless ramp of height $$h$$ and then moves along a horizontal surface with friction coefficient $$\mu. $$What is the speed of the block just before it starts to slow down due to friction?

Accepted Answer

$$\sqrt{2gh}$$

Question 5

A satellite of mass $$m$$ orbits the Earth at a radius $$r$$ with period $$T. $$What is the expression for the satellite's speed $$v$$?

Accepted Answer

$$v = \sqrt{\dfrac{GM_E}{r}}$$

Question 6

A block of mass $$m is $$attached to a spring with spring constant $$k$$ and oscillates on a frictionless surface. What is the period of oscillation?

Accepted Answer

$$T = 2\pi \sqrt{\dfrac{m}{k}}$$

Question 7

A stone is thrown upward from the ground with initial speed $$v_0 on a $$planet with unknown gravity $$g. It $$returns to the ground after $$T$$ seconds. What is the value of $$g in $$terms of $$v_0$$ and $$T$$?

Accepted Answer

$$g = \dfrac{2v_0}{T}$$

Question 8

A block of mass $$m$$ slides down a frictionless loop-the-loop of radius $$R. $$What is the minimum height $$H_{min}$$ above the bottom of the loop from which the block must be released to just complete the loop?

Accepted Answer

$$H_{min} = \dfrac{5}{2}R$$

Question 9

A car of mass $$m$$ moves at speed $$v$$ over the top of a hill of radius $$r. $$What is the normal force on the car at the top of the hill?

Accepted Answer

$$N = mg - \dfrac{mv^2$}{r}$$

Question 10

A block of mass $$m is $$floating in water. The density of the block is $$\rho_b$$ and the density of water is $$\rho_w. $$What fraction of the block's volume is submerged?

Accepted Answer

$$\dfrac{\rho_b}{\rho_w}$$

Question 11

A viscous fluid is flowing through a horizontal pipe of constant cross-section. According to Bernoulli's principle, how does the pressure at a point where the speed is higher compare to a point where the speed is lower?

Accepted Answer

The pressure is lower where the speed is higher.

Question 12

A block of mass $$m is $$projected up a rough incline with initial speed $$v_0. $$The coefficient of kinetic friction is $$\mu_k. $$What is the distance $$d$$ the block travels up the incline before coming to rest?

Accepted Answer

$$d = \dfrac{v_0$^2}{2g(\sin	heta + \mu_k \cos	heta)}$$

Question 13

A volleyball player hits a ball at height $$H$$ above the ground with initial speed $$v_0 at $$angle $$	heta$$ above the horizontal. Neglecting air resistance, what is the time $$t it $$takes for the ball to reach the same height $$H$$ again?

Accepted Answer

$$t = \dfrac{2v_0 \sin	heta}{g}$$

Question 14

A block of mass $$m is $$attached to a horizontal spring and oscillates with amplitude $$A. $$What is the total mechanical energy of the system?

Accepted Answer

$$E = \dfrac{1}{2}kA^2$

Question 15

A car of mass $$m is $$moving in a circle of radius $$r at $$constant speed $$v. $$What is the magnitude of the friction force required to keep the car moving in a circle?

Accepted Answer

$$F = \dfrac{mv^2$}{r}$$

Question 16

A block of mass $$m is $$dropped from height $$h$$ onto a spring with spring constant $$k. $$What is the maximum compression $$x_{max} of $$the spring?

Accepted Answer

$$x_{max} = \dfrac{mg + \sqrt{(mg)^2$ + 2mkh}}{k}$$

Question 17

A block of mass $$m is $$moving with velocity $$v$$ and collides elastically with a stationary block of mass $$2m. $$What is the velocity of the first block after the collision?

Accepted Answer

$$v' = -\dfrac{v}{3}$$

Question 18

A stone is thrown horizontally from a height $$h$$ with speed $$v_0. $$Neglecting air resistance, what is the time it takes to hit the ground?

Accepted Answer

$$t = \sqrt{\dfrac{2h}{g}}$$

Question 19

A block of mass $$m is at $$rest on a horizontal surface. A force $$F is $$applied at an angle $$	heta$$ above the horizontal. What is the normal force on the block?

Accepted Answer

$$N = mg - F\sin	heta$$

Fundamental Concepts and Problems in College Physics: Mechanics and Fluids

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